scholarly journals Optimal Control of an SIR Model with Delay in State and Control Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Elhia ◽  
Mostafa Rachik ◽  
Elhabib Benlahmar
Keyword(s):  
Optimal Control ◽  
Influenza A ◽  
Optimization Strategy ◽  
Sir Epidemic Model ◽  
Optimal Control Strategy ◽  
Control Variables ◽  
Sir Epidemic ◽  
Influenza A H1n1 ◽  
Using Data ◽  
And Control

We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.

CHAOS ANALYSIS AND CONTROL FOR A CLASS OF SIR EPIDEMIC MODEL WITH SEASONAL FLUCTUATION

2013 ◽  
Vol 06 (01) ◽  
pp. 1250063 ◽  
Author(s):  
YI ZHANG ◽  
QINGLING ZHANG ◽  
FUZHEN ZHANG ◽  
FENGLAN BAI
Keyword(s):  
Epidemic Model ◽  
Influenza A ◽  
Control Method ◽  
Seasonal Fluctuation ◽  
H1n1 Influenza ◽  
Sir Epidemic Model ◽  
Chaotic Motions ◽  
Sir Epidemic ◽  
The Common ◽  
And Control

In this paper, the problems of chaos and chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be disappeared. Finally, numerical simulations illustrate that the controller is effective.

Strategies to enhance the biodegradation of toxic compounds using discontinuous processes

2001 ◽  
Vol 43 (3) ◽  
pp. 283-290 ◽  
Author(s):  
G. Buitrón ◽  
G. Soto ◽  
G. Vite ◽  
J. Moreno
Keyword(s):  
Optimal Control ◽  
Activated Carbon ◽  
Dissolved Oxygen ◽  
Batch Reactor ◽  
Biological Degradation ◽  
Optimal Control Strategy ◽  
Measured Variable ◽  
Time Optimal ◽  
High Concentrations ◽  
And Control

This study presents two strategies used to enhance the biological degradation of phenolic wastewaters. In the first one the operation of a sequencing batch biofilter added with granular activated carbon (SBB-AC) was studied. The second strategy presents the results of the automation of a sequencing batch reactor in order to optimize the reaction phase. In this case, the dissolved oxygen was employed to monitor and control the reactor. The results of the SBB-AC system, based on the configuration of the reactor, type and size of activated carbon and size of the packing material, are discussed. The system biodegraded efficiently (total phenol removals as high as 97%) high concentrations (600 mg/l) of a mixture of phenol, 4-chlorophenol, 2,4-dichlorophenol and 2,4,6-trichlorophenol. Maximal eliminated loads of 4.33 kg COD/m3-d were achieved. For the second strategy, the applicability of an optimal control for a SBR using the dissolved oxygen as the measured variable was demonstrated. When the reactor was operated under the time-optimal control strategy, the degradation time of 4-chlorophenol was reduced. A very satisfactory operation of the reactor was observed, since the removal efficiencies were around 99%.

scholarly journals Optimal control of a SIR epidemic model with general incidence function and a time delays

Cubo (Temuco) ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 53-66 ◽  
Author(s):  
Moussa Barro ◽  
Aboudramane Guiro ◽  
Dramane Ouedraogo
Keyword(s):  
Optimal Control ◽  
Epidemic Model ◽  
Time Delays ◽  
Sir Epidemic Model ◽  
Incidence Function ◽  
Sir Epidemic

An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions

2020 ◽  
Author(s):  
Ali Ketabdari ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Operational Matrix ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Control Variables ◽  
Fractional Optimal Control ◽  
Bernstein Functions ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract We define a new operational matrix of fractional derivative in the Caputo type and apply a spectral method to solve a two-dimensional fractional optimal control problem (2D-FOCP). To acquire this aim, first we expand the state and control variables based on the fractional order of Bernstein functions. Then we reduce the constraints of 2D-FOCP to a system of algebraic equations through the operational matrix. Now, one can solve straightforward the problem and drive the approximate solution of state and control variables. The convergence of the method in approximating the 2D-FOCP is proved. We demonstrate the efficiency and superiority of the method by comparing the results obtained by the presented method with the results of previous methods in some examples.

scholarly journals Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

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